Year 10 Surds Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 indices & scientific notation worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Indices & Scientific NotationYear 10 Surds Worksheet — Level 1 — Practice Set 4 — Answers
Write each answer in simplest surd form: √a × √b = √(ab), and look for square factors (4, 9, 16, 25, 36…).
1.Simplify √48.
Answer: 4√3
- 48 = 16 × 3
- √48 = √16 × √3 = 4√3
2.Simplify √12.
Answer: 2√3
- 12 = 4 × 3
- √12 = √4 × √3 = 2√3
3.Simplify √75.
Answer: 5√3
- 75 = 25 × 3
- √75 = √25 × √3 = 5√3
4.Simplify √27.
Answer: 3√3
- 27 = 9 × 3
- √27 = √9 × √3 = 3√3
5.Simplify √45.
Answer: 3√5
- 45 = 9 × 5
- √45 = √9 × √5 = 3√5
6.Simplify √468.
Answer: 6√13
- 468 = 36 × 13
- √468 = √36 × √13 = 6√13
7.Simplify √176.
Answer: 4√11
- 176 = 16 × 11
- √176 = √16 × √11 = 4√11
8.Simplify √99.
Answer: 3√11
- 99 = 9 × 11
- √99 = √9 × √11 = 3√11
9.Simplify √126.
Answer: 3√14
- 126 = 9 × 14
- √126 = √9 × √14 = 3√14
10.Simplify √96.
Answer: 4√6
- 96 = 16 × 6
- √96 = √16 × √6 = 4√6
11.Simplify √135.
Answer: 3√15
- 135 = 9 × 15
- √135 = √9 × √15 = 3√15
12.Simplify √117.
Answer: 3√13
- 117 = 9 × 13
- √117 = √9 × √13 = 3√13
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.